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Strangerrr

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Registered: 2018-07-28

Posts: 23

Inductive and Deductive Reasoning

Use the following scenario for questions 14 and 15.

     Imagine you have been called as a expert witness in a court case.  Your expertise is in the area of planes (not airplanes, just planes in geometry).  You have been asked the following questions.  Your task is to convince the jury that there is, in fact, a plane.  You must prove all three of the definitions of a plane given in Lesson 1.  You may need to include some other definitions such as the definition of an angle, a ray, etc.

14.  Question from the lawyer:  "Dr. Expert, I only see three parallel lines here.  Terry said that having these three parallel lines mean you have at least one plane.  I enter Exhibit A which shows three definitions of a plane.  From what I see, none of these definitions say that three parallel lines define a plane.  Explain how the definitions in Exhibit A prove that you have at least one plane given three parallel lines."   (This question is worth 3 points.)

15.  Question from the lawyer:  "Dr. Expert, I only see an angle between 0° and 180° here.  Kelly said that having this angle means you have a plane.  I enter Exhibit A which shows three definitions of a plane.  From what I see, none of these definitions say that an angle defines a plane.  Explain how the definitions in Exhibit A prove that an angle defines a plane."   (This question is worth 3 points.)

I kept getting these questions wrong and so the questions changed to :

14 a - Three points are noncollinear if they do not form a line. Where would you place three distinct points using three parallel lines to ensure that the points were noncollinear. It may be easier to draw a picture first. Then we can work on describing the situation.

14 b - Try drawing a picture for this one as well. Using three parallel lines (or less) show you have a line and a point not on that line.

15 a-b - try the same things with using pictures.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Inductive and Deductive Reasoning

hi Strangerrr

Draw three distinct, parallel lines and another line (a transversal) to cross them all.  Let's say it cuts them at points A, B and C.  Choose any other point on the third parallel that is not C, say D.  Then A, B and D are non colinear.

The parallel through A is a 'line' and any of B, C and D may be chosen as a point not on that line.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Alg Num Theory

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Registered: 2017-11-24

Posts: 693

Website

Re: Inductive and Deductive Reasoning

Draw three distinct, parallel lines and another line (a transversal) to cross them all.

But those three lines may not be in one and the same plane.

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Me, or the ugly man, whatever (3,3,6)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Inductive and Deductive Reasoning

Thanks Alg Num Theory.  Hadn't thought of that.

But I think I can modify the plan to cover this.  Draw a plane that intersects the three lines in A, B and C.  Then choose D on that line as any point other than C.  Then as before.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob